Effect of reflux ratio — As the reflux ratio in a distillation column is increased from its minimum value, which overall trend is correct?

Introduction:
Reflux ratio is a key design and operating variable in distillation. Moving away from minimum reflux reduces the number of equilibrium stages, but also increases internal flows and energy use. Understanding these trade-offs is crucial for selecting an economical design point.

Given Data / Assumptions:

• Constant product specifications.
• Feasible range: from minimum reflux (infinite stages) to very high reflux (near total reflux, minimal stages).
• Typical cost structure: capital linked to plate count/size; operating linked to reboiler/condenser duties.

Concept / Approach:
As reflux increases from the minimum, the number of stages decreases sharply at first and then with diminishing returns. Capital cost initially falls (fewer trays/shorter column), but energy and utility costs rise due to increased internal liquid and vapor rates. The combined total annual cost therefore shows a shallow minimum at an intermediate reflux ratio.

Step-by-Step Solution:
At minimum reflux: N → very large, capital high, energy low.Increase reflux slightly: N drops rapidly; capital decreases.Further increases: N decreases slowly; utilities rise significantly.Result: a cost optimum where total annual cost is minimized.

Verification / Alternative check:
Gilliland correlations (or modern simulators) show diminishing returns in stage reduction at high reflux, consistent with the cost-tradeoff curve.

Why Other Options Are Wrong:

• (a) The stripping-line slope is not the primary monotonic trend with reflux; rectifying line slope increases.
• (b) Trend is opposite: decrease is rapid at first, then slower.
• (d) Both internal liquid and vapor generally increase with reflux for fixed separation.
• (e) Minimum plates occur at very high (approaching total) reflux, not at minimum reflux.

Common Pitfalls:
Assuming linear trade-offs; ignoring condenser and reboiler size impacts at high reflux.

Final Answer:
The total annual cost first decreases (as plates fall) and then increases (as utilities rise), giving an optimum